The carnage in Afghanistan has continued unabated on a major Muslim holiday, as attackers killed two pairs of brothers with links to the government, and three NATO service members.

The targeted killings are part of a spate of similar attacks on those associated with the government, further complicating efforts by international forces in country to hand over security responsibility to Afghans as foreign combat troops withdraw.

In the first attack, a bomb hidden in a cemetery in the southern province of Helmand killed a police chief and his brother who were visiting a family grave for the Eid al-Fitr holiday.

Seven of the men's family members were wounded in the early-morning blast in the provincial capital of Lashkar Gah, said Helmand Deputy Police Chief Ghulam Rabbani.

No one immediately claimed responsibility, but the attack was consistent with the Taleban's strategy to target authorities and others who align themselves with the government or international forces.

The two men were brothers of a lawmaker for Helmand province, Abdulwadood Popal, who was not at the cemetery at the time of the blast.

The family was visiting the grave after attending a morning prayer service for the holiday, which ends the month-long Ramadan fasting period.

Later on in the western Farah province, gunmen on a motorcycle opened fire on the car of an intelligence service official as he was driving home from a family visit, killing him and his brother who worked for the customs service.